Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Fracture and viscoelastic properties of asphalt binders during fatigue and rest periods

Viscoelastic asphalt binder plays an important role in bonding individual aggregate particles and contributes to the durability and stability of asphalt pavement. When asphalt binder is subjected to cyclic loading, deformation and fracture may develop simultaneously within it, leading to the deterioration of material properties and eventually fatigue failure. Research has found that some degree of recovery may develop if rest periods are applied after fatigue deterioration. However, it is not clear whether such recovery is caused by fracture healing, viscoelastic recovery, or both. This paper presents an analysis to differentiate the contributions of fracture healing and viscoelastic recovery to the asphalt binder during rest periods. It also evaluates the damage caused by deformation and fracture during a fatigue process. It is found that viscoelastic recovery plays an important role in the instant increase in the dynamic shear modulus at the beginning of the rest period. The effect of fracture healing on dynamic shear modulus recovery is more dominant in the long term. A healing index is developed based only on the fracture healing of asphalt binder, excluding the effect of viscoelastic recovery. It can be used to evaluate the true healing properties of different asphalt binders. Copyright © 2014 by ASTM International.

Anisotropic viscoelastic properties of undamaged asphalt mixtures

A test protocol and a data analysis method are developed in this paper on the basis of linear viscoelastic theory to characterize the anisotropic viscoelastic properties of undamaged asphalt mixtures. The test protocol includes three nondestructive tests: (1) uniaxial compressive creep test, (2) indirect tensile creep test, and (3) the uniaxial tensile creep test. All three tests are conducted on asphalt mixture specimens at three temperatures (10, 20, and 30°C) to determine the tensile and compressive properties at each temperature and then to construct the master curve of each property. The determined properties include magnitude and phase angle of the compressive complex modulus in the vertical direction, magnitude and phase angle of the tensile complex modulus, and the magnitude and phase angle of the compressive complex modulus in the horizontal plane. The test results indicate that all tested asphalt mixtures have significantly different tensile properties from compressive properties. The peak value of the master curve of the tensile complex modulus phase angle is within a range from 65 to 85°, whereas the peak value of the compressive moduli phase angle in both directions ranges from 35 to 55°. In addition, the undamaged asphalt mixtures exhibit distinctively anisotropic properties in compression. The magnitude of the compressive modulus in the vertical direction is approximately 1.2 to ̃2 times of the magnitude of the compressive modulus in the horizontal plane. Dynamic modulus tests are performed to verify the results of the proposed test protocol. The test results from the proposed test protocol match well with those from the dynamic tests. © 2012 American Society of Civil Engineers.

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

Energy-based damage and fracture framework for viscoelastic asphalt concrete

A framework based on the continuum damage mechanics and thermodynamics of irreversible processes using internal state variables is used to characterize the distributed damage in viscoelastic asphalt materials in the form of micro-crack initiation and accumulation. At low temperatures and high deformation rates, micro-cracking is considered as the source of nonlinearity and thus the cause of deviation from linear viscoelastic response. Using a non-associated damage evolution law, the proposed model shows the ability to describe the temperature-dependent processes of micro-crack initiation, evolution and macro-crack formation with good comparison to the material response in the Superpave indirect tensile (IDT) strength test.

Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model

This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.